A case could be made for DS9 being highly influential on the shows that have aired since. It's not so much its fame but its format, which has dominated television in the past two decades. There has been a greater focus on TV since DS9 on character-based drama and serialization. I think DS9 has a lot to do with that. For that reason, numerous shows today can trace a direct line to DS9 much more easily than the other Trek shows. Even sitcoms have skewed toward doing things DS9 was doing 20 years ago.
I would say TNG is highly influential as a show that popularized first-run syndication, and TOS as a show that, along with The Twilight Zone popularized relatively grownup science fiction for television. TOS also helped popularize shows with diverse teams.
Though I'm warming up on ENT, I wouldn't say it's influential. Nor would I say VOY is.